Syntactically correct, at least in the first example, would be ist, since 'Nüsse' only qualifies 'Menge' further (a quality of what). But if you want to emphasize that it's a lot of nuts, using sind isn't out of place.

Please note though, that this doesn't apply when you turn the sentence upside down. You will likely see

Das ist eine Menge Nüsse.

As you can see, the tendency is actually to go with the part of the noun expression which is closest to the verb.

Your second example is somewhat different, because it uses a relative clause. If you use the singular in this case, you're stressing the amount, and if you use the plural, you're stressing the diversity of information. Something similar to quantity vs. quality.

"sind" is clearly out of place. It is one set of nuts ("eine Menge Nüsse"), not two different ones. So the singular form must be used. The reference to the German wikipedia entry on Constructio_ad_sensum is not helping as that entry is giving bad examples as well.
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ToschoApr 24 '13 at 13:51

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@Toscho "sind" is clearly not out of place. First, you find a lot of Google hits for both plural and singular. Second, even Duden has an example where they use both plural and singular. Third, from my personal experience: it sounds absolutely ugly to use singular and I cannot remember that I ever heard that before. But from Internet search it seems to me to be valid to go with both variants so probably different usages in different parts of Germany.
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Em1Apr 24 '13 at 13:58

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I don't know how this syntactic aspect in the dealt with in the different dialects, but in standard German, it is fixed. Please give the Duden example.
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ToschoApr 24 '13 at 14:08

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@Toscho, even Duden itself recognises this as a construction (not saying whether it is valid is not): duden.de/rechtschreibung/Constructio_ad_Sensum. Not even speaking about the multicultural significance of this construction (used as a figure of speech in Latin and ancient Greek poetry). In addition, I would be really careful using words like clearly or must in the context of language usage. A language rarely has real musts or clears. Teaching a person to speak like a dictionary will most likely earn them scorn or contempt in the eyes of many native speakers.
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user2311517Apr 24 '13 at 14:36

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@ThorstenDittmar with the funny outcome that as far as communication is concerned, rules are bent as needed to make communication more simple and convenient. I wasn't trying to say there are no rules at all: I was saying it's dangerous to have a black-and-white attitude. Example: We will both agree that "Da kann ich nichts für." isn't really very correct High German. And still, I hear it at work a lot more often then "Dafür kann ich nichts." Why? Because it's a lot more lively.
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user2311517Apr 24 '13 at 14:51

The verb goes with the subject of the sentence - and the subject in your example is "eine Menge". Since "eine Menge" is only "one", the correct form is ist.

A common mistake that's currently spreading like a virus in the German language is not to mind the number of subjects, like "Schon jetzt wird 30 Prozent der Energie von Windkrafträdern gedeckt", which is wrong, because the subject ("30 Prozent der Energie") is really a plural (1% would be singular, 2% onwards are plural), so they "werden gedeckt".

Your second sentence in the first example is actually not clear. The verb in the relative clause may either refer to the "Menge" or the "Kontextinformationen", if the relative clause is to define which "Kontextinformationen" are in the "Menge".

Your example is one dimensional: "Das Essen und das Trinken war gut." is a correct sentence. The subject is not "das Essen und Trinken", but there are two subjects "das Essen" und "das Trinken" sharing the same rest of the sentence ("zusammengezogener Satz").
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ToschoApr 24 '13 at 13:44

Your argumentation on the second example is one dimensional: If the relative pronoun refers to "Menge", than the verb must be in singular form. If the relative pronoun refers to "Kontextinformationen", than the verb must be in plural form. Both are possible.
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ToschoApr 24 '13 at 13:46

@Toscho: I agree on the first "Essen und Trinken" example - I'll try to find a better one. The "Kontextinformationen" however is pretty clear - the relative pronoun refers to "Menge", not "Kontextinformationen", so it is "die Menge, die notwendig ist".
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Thorsten DittmarApr 24 '13 at 13:56

Your new example is correct, but you still have a mistake: The subject is not "30 Prozent" but "30 Prozent der Energie". Your explanation has some issues as well, as 30% is less than 1, but you say that 30% is more than "one thing". It's better to say, that it's more than 1%.
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ToschoApr 24 '13 at 14:23

For the first example, the singular form must be used, as the verb always refers to the noun of the sentence and is conjugated according to it. The subject of the sentence is eine ganze Menge Nüsse so the verb sein must be conjugated as ist. → Eine ganze Menge Nüsse ist das. (You can change the subject to das if you want to, but it wouldn't change anything, as the demonstrative pronoun das inherits its properties from the noun referred to, which is eine ganze Menge Nüsse as well.)

In the second example, both forms ist and sein are possible, depending on what noun the relative pronoun die refers to. If it refers to Menge, than the singular form ist must be used (see above). If it refers to Kontextinformationen, which is a plural, than the plural form sein must be used.

The difference to the first example is, that a relative pronoun can refer to any previous noun, the verb only refers to the subject.

The relative pronoun in the second example can never refer to "Kontextinformationen" as "der Kontextinformationen" only qualifies "die Menge" and is not a standalone subject in that sentence. So it is clear that the relative pronoun refers to "die Menge" and thus implies the use of "ist".
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Thorsten DittmarApr 24 '13 at 14:38

You're right about the relative pronouns. Actually, we should talk about the verbs. In the example the OP provided, there are two possible meanings: The relative clause may define which "Kontextinforationen" are in the "Menge" (die Informationen, die notwendig sind), or it defines that the "Menge ist notwendig" (die Menge, der ..., die notwendig ist). More interesting is how the sentence continues: what's happening to the "Menge"? And here the verb must clearly refer to the "Menge" (Singular). You can't say: "Die Menge der ..., die notwendig sind, müssen..."
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Thorsten DittmarApr 25 '13 at 11:55

I've also updated my answer to make this clearer.
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Thorsten DittmarApr 25 '13 at 12:00